Mathematical Sciences: Geometric Approach to Weinstein Conjecture

主要研究者将研究紧接触流形的接触叶中紧叶的存在性。这些叶状物的存在是温斯坦推测的。这位调查员和其他数学家已经解决了几个特殊的案件。Lickorish手术技术将被用来调查这个问题的三维版本。将Okumura的理论应用于Kaehler流形中具有接触型的超曲面的情况。此外，还将研究微分同胚群。“流形”是广义曲面。这些可能被较低维度的“叶子”的集合所填充。这样的树叶集合被称为“树叶”。首席研究人员将研究那些不会连续包裹但实际上是近距离包裹的叶子。这些树叶在文献中被称为“紧凑型叶子”。这在其他科学的应用中尤其重要，因为它们在一般意义上代表着无限重复的行为。

The principal investigator will study the existence of compact leaves in contact foliations of compact contact manifolds. The existence of these foliations was conjectured by Weinstein. Several special cases have been solved by this investigator and by other mathematicians. Lickorish surgical techniques will be used to investigate the three-dimensional version of the problem. Okumura's theory will be applied to the problem in the case of hypersurfaces with contact types in Kaehler manifolds. Diffeomorphism groups will also be studied. "Manifolds" are generalized surfaces. These may be filled with collections of lower dimensional "leaves." Such collections of leaves are called "foliations." The principal investigator will study leaves which do not wrap on continuously but actually close up. These are called in the literature, "compact leaves." Such are particularly important in applications to other sciences in that they represent, in a general sense, behavior which repeats indefinitely.